Course Modules for First Year B.A. Mathematics
MODULE CODE: MH4731
MODULE TITLE: Elementary Number Theory
PREREQUISITE MODULE(S): None
OBJECTIVES:
Number theory is a foundational branch of mathematics. This module gives the student a solid grounding in the subject.
LEARNING OUTCOMES:
Students who successfully complete this module should be able to:
- understand the basic elements of number theory;
- understand notation and conventions associated with the topic;
- use known algorithms to solve problems related to divisibility;
- master modular arithmetic;
- produce coherent and convincing arguments;
- communicate solutions to problems clearly and coherently.
MODULE CONTENT:
- Representations of numbers;
- The binomial theorem; Mathematical induction;
- Divisibility of integers; Prime Numbers and The Fundamental Theorem of Arithmetic;
- Euclid's algorithm
- Congruence; linear Diophantine equations; Fermat's Little Theorem; Using congruences to solve more complex problems;
- Pythagorean Triples.
PRIME TEXTS:
ORE, O. (1969). Invitation to Number Theory. Mathematical Association of America.
SILVERMAN , J. H. (2012). A Friendly Introduction to Number Theory. Pearson Education.
OTHER RELEVANT TEXTS:
NIVEN, I.M., ZUCKERMAN, H.S. (1980). An introduction to the theory of numbers, Wiley.
DUDLEY, U. (2008). Elementary Number Theory, Dover.
BURN, R.P. (1997). A pathway into number theory, Cambridge University Press.
FORMAN, S., RASH, A. (2015). The Whole Truth About Whole Numbers, Springer.
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MODULE CODE: MH4722
MODULE TITLE: Introduction to Geometry
PREREQUISITE MODULE(S): None
OBJECTIVES:
Geometry is a core part of mathematical education, because it provides a paradigm of rigorous mathematical reasoning. This module equips students with basic knowledge and skills of euclidean geometry. It thereby prepares the student for the study of other areas of mathematics.
LEARNING OUTCOMES:
Students who successfully complete this module should be able to:
- understand, express and use geometric results;
- carry out geometric constructions;
- determine certain geometric quantities from others;
- use coordinates to solve geometric problems analytically.
MODULE CONTENT:
- angle, distance, length, area;
- coordinates;
- lines, triangles and circles;
- geometric constructions;
- congruence and similarity.
PRIME TEXTS:
OSTERMANN, A., WANNER, G. (2012). Geometry by Its History, Springer.
LANG, S., MURROW, G. (1988). Geometry, Springer.
GARDINER, A. D., BRADLEY, C. J. (2005). Plane Euclidean Geometry: Theory and Problems, The United Kingdom Mathematics Trust.
OTHER RELEVANT TEXTS:
BRUMFIELD, C. F., VANCE, I. E. (1970). Algebra and Geometry for Teachers, Addison-Wesley.
CLARK, D. M. (2012). Euclidean Geometry: A Guided Inquiry Approach, American Mathematical Society.
